Archive of posts in May, 2023
Suppose there are distinguishable boxes and indistinguishable balls. Now, we randomly put the balls into the boxes. For each of the boxes, what is the probability that it contains balls? This is a simple combanitorics problem that can be solved by the stars and bars method. It turns out that in the limit with fixed, the distribution tends to be a geometric distribution.
gotocan also do this easily. However, in most other languages, it is not easy to break out of nested loops. I want to introduce a way to do this in Ruby.
I set up a simple model to determine the production and consumption in free trade between nations.
For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.